Preheat your oven to 400 degrees F. Grease a baking pan (a rimmed baking sheet or anything your fish will fit into) with cooking spray.
Rinse the salmon under cold water and feel for any bones to remove. Pat the fish dry with paper towels.
Place the salmon in your pan (skin side down) and top each piece of fish with one teaspoon of olive oil. Brush the oil or use your fingers to spread it evenly. (Wash your hands if you touched the raw fish.) Sprinkle salt and pepper on the salmon.
Slice the fresh mozzarella into rounds about ¼ inch thick, but no more than ½-inch thick. Place two slices of mozzarella on each piece of salmon, in a single layer. (If the fish is longer, you might be able to fit three slices of cheese.)
Rinse the tomatoes and pat them dry. Slice them in half, then in half again if large. Place the tomatoes on top of the mozzarella, distributing them across each piece of fish. Sprinkle the tomatoes with garlic powder and black pepper. (You shouldn't need any more salt, since the cheese is salty.)
Bake the salmon for 20 minutes, or until the fish can be flaked with a fork. If the salmon is thin (such as wild salmon) it might take just 15 minutes.
While the salmon is in the oven, rinse and pat dry the basil leaves. Trim off the stems. Make ribbons of basil by rolling up each leaf and then slicing it into sections about ¼-inch thick.
To serve, remove the skin (if any) from the bottom of the fish by inserting a spatula between the skin and the salmon. Lift the fish right off the skin. Top each piece of salmon with basil ribbons and drizzle on balsamic glaze.
Store leftovers in a sealed container in the refrigerator for up to four days.
Video
Notes
Fresh mozzarella is white and contains more moisture than regular mozzarella. Fresh mozzarella's texture and slightly salty flavor work better here than regular mozzarella.